Silly question about round kicks, kicking side arm up or down?

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When I was first shown the round in kick in Karate/TSD, I was taught to keep the hands up at all times. Once I started Enshin (Kyokushin off shoot), I was taught the whole kicking side arm drops to help with something, I don't really know. Now that I've started Muay Thai the kicks are pretty much the same, drop kicking side arm, shin contact etc, hip rotation etc.

So last night I'm doing some padwork at my judo club, and one of the Judo blackbelts tells me to keep my hands up when I throw my kick. I basically ask why should I do that when I've been taught this way (dropping kicking side arm) by 2 different schools, plus have seen actual Thai fighters do this on numerous videos. He said he trained in Thailand and with someone else is Virginia, and that they don't drop their arms. Now I personally believe that he has trained with them, I just completely disagree with him as far as not dropping that arm. Also despite my disagreement I have no problem with learning a new way to kick, just not a month before a fight]

So what does this come down to personal preference or statistical proof?

i don't understand how dropping the hand "in the opposite direction" of the kick creates any more power... of course i am no physicist, but it seems back asswards to me... wouldn't it in fact take power/momentum away from the kick?... i keep the hands up... alot of guys i mess around with try to catch/block the kick with the same side hand and launch a big ass punch with the other hand... so i use the "up hand" to defend/counter this

Swinging the arm does seem to generate more power. I suspect it makes it a little easier to turn your body into the kick.

Keeping your hands up in a guard position tends to get them in the way and **** up peoples kick because they now cant rotate as efficiently and thus rob themselves of power.

My prefered way is to shove my hand in their face and thus they see nothing coming.

I also have a cool sweep that I like to do that plays off a similar concept. Shoving the hand to the side of their head like you were going to kick them, and then using the hand to kindof pull their head towards your right (assuming you're orthodox) and then kick their feet out from under them.

again wouldn't moving your arm and shoulder in the opposite direction actually LIMIT the amount of hip rotation you can achieve AND likely destroy your balance since your upper body and lower body are rotating in opposite directions... i have done it both ways and i quite like your cool sweep, but i have settled on hands up or at least dropping only slightly... i would still like to see what others think since i DO in fact drop it somewhat when facing someone in a 'MIRROR" stance... that is me fighting a southpaw who tries to kick my kick or my supporting leg

i hear what you're saying i have seen it practiced/taught both ways just seems kind of backwards to me to drop it... whatever works for someone is good just make sure you don't get the habit and have someone use it against you... my case for dropping slightly was some long legged southpaw guy who would kick over my low roundhouse into my ribs BECAUSE i kept my hands high so i modified it a little to protect my ribs from southpaws ( or vice versa when i go southpaw)... guys are always picking up my habits and using them against me, but well i do that too so...

Though it may seem counter-intuitive, throwing the arm should actually help generate more power (though, anyone that knows for sure should feel free to tear me apart for not knowing my dynamics). In order to throw that hand back, you have to have an equal force going forward due to Newton's Third Law. Since you drop your hand in the same plane (but opposite direction) of your kick, the end result is more force.

Once again, this is coming from a chemical engineering student that took physics I over 2 years ago, so i could very well be wrong.